Vampire's drink!
Albert is an immortal vampire who drinks blood every 4 days. Which of the following is true about the probability that the one day selected randomly out of random set of consecutive days did he drink blood?
Note: Consider that for any n you choose Albert has lived very much longer than that!
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1 solution
The probability that he drinks blood on a day is 1/4. This problem can be solved by taking 4 cases: n is of the type 4m,4m+1,4m+2,4m+3. If you consider number of such days in each case is either m or m+1 the probability always comes out to be 1/4. For n=4m+2 I am proving:
m days:1/2 probability (either 3rd or 4th is the blood day of the first four)
m+1 days: 1/2 probability (either 1st or 2nd is blood day out of the first four)
Probability=((1/2)X(m/(4m+2))+(1/2)X((m+1)/(4m+2)))=1/4